US5467404A - Method and apparatus for contrast enhancement - Google Patents

Method and apparatus for contrast enhancement Download PDF

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US5467404A
US5467404A US07/924,095 US92409592A US5467404A US 5467404 A US5467404 A US 5467404A US 92409592 A US92409592 A US 92409592A US 5467404 A US5467404 A US 5467404A
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image
detail
images
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Pieter P. Vuylsteke
Emile P. Schoeters
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Agfa HealthCare NV
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    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00—Image enhancement or restoration
    • G06T5/20—Image enhancement or restoration using local operators
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00—Image enhancement or restoration
    • G06T5/10—Image enhancement or restoration using non-spatial domain filtering
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00—Image enhancement or restoration
    • G06T5/90—Dynamic range modification of images or parts thereof
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/20—Special algorithmic details
    • G06T2207/20016—Hierarchical, coarse-to-fine, multiscale or multiresolution image processing; Pyramid transform
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/20—Special algorithmic details
    • G06T2207/20021—Dividing image into blocks, subimages or windows
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/20—Special algorithmic details
    • G06T2207/20048—Transform domain processing
    • G06T2207/20064—Wavelet transform [DWT]

Definitions

  • This invention relates to an image contrast enhancement method and to an apparatus for enhancing the contrast of a digital image. More in particular it relates to such method for use in a medical radiographic imaging system, such as a computed radiography system or a computed tomography system.
  • pyramidal image processing In the field of digital image processing a novel paradigm of multiresolution computation has evolved the last decade, sometimes called pyramidal image processing. According to this concept multiple sets of processing parameters are used, tuned to a wide range of detail sizes.
  • the basic concepts and efficient implementations of pyramidal decomposition are described in: Burr P. J., "Fast Filter Transforms for Image Processing", Computer Graphics and Image Processing, vol. 16, pp. 20-51, 1981; Crowley J. L., Stern R. M., “Fast Computation of the Difference of Low-Pass Transform", IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 6, no. 2, March 1984.
  • Another object of the present invention is to provide a method for reducing the dynamic range without lowering the contrast of low amplitude details, so that the whole range of signal levels may be visualised on a display or recorded on a recording film with acceptable contrast.
  • Another object of the present invention is to provide a method for enhancing contrast without preference for a specific detail size range.
  • a further object of the present invention is to provide a method for enhancing contrast without creating artifacts in the neighborhood of significant image transitions, typical of methods related to unsharp masking or adaptive histogram equalisation.
  • a still further object of the present invention is to provide a method for enhancing contrast without remarkably boosting the noise component.
  • a still further object of the present invention is to provide a method for enhancing contrast with increased sharpness.
  • a still further object of the present invention is to provide an apparatus for enhancing contrast with the above mentioned features.
  • each pixel value in said original image is equal to the sum of the corresponding pixel value of said residual image incremented by the corresponding pixel value of each of said detail images, said residual and detail images being brought into register with the original image by proper interpolation if their number of pixels is not equal to the number of pixels of the original image, and so that
  • the spatial frequency of every detail image is limited to a specific frequency band, said frequency band being defined as the compact region in the spatial frequency domain which contains nearly all (say 90%) of the spectral energy of the basic frequency period of said discrete detail image, adjusted to the original spatial frequency scale if said detail image contains less pixels than said original image;
  • every detail image corresponds to a different spatial frequency band, in such a way that the entire spatial frequency domain ranging from -pi to pi radians per pixel along both spatial frequency axes is covered by said spatial frequency bands associated with all said detail images considered within the decomposition;
  • each spatial frequency band associated with one of said detail images may partially overlap the neighboring bands without being fully included by a frequency band associated with another detail image;
  • the number of pixels within each detail image is at least the number of pixels required by the Nyquist sampling criterion, so as to avoid aliasing
  • the processed image is computed as the pixelwise sum of all modified detail images incremented by the corresponding pixel value in the residual image, said residual and detail images being brought into register with the original image by proper interpolation if their number of pixels is not equal to the number of pixels of the original image.
  • said transform yielding a set of detail coefficients each expressing the relative contribution to the original image of one of a set of basis functions representing said basic detail images and a residual coefficient representing the relative contribution to the original image of a basis function representing said basic residual image, whereby said basis functions are continuous and non-periodic and have zero mean value except for the basis function that represents the basic residual image, and wherein said transform is characterised in that there exists an inverse transform which returns the original image or a close approximation thereof when being applied to said transform coefficients,
  • the decomposition is such that the value of each pixel within said original image is equal to the sum of all corresponding pixel values in said basic detail images multiplied by the associated detail coefficient, said sum further incremented by the corresponding pixel value of said basic residual image multiplied by the associated residual coefficient, and wherein the decomposition is such that if the complete set of said predetermined basic detail images would be partitioned into subsets of basic detail images with identically sized spatial extent, said spatial extent being defined as the compact pixel domain which contains all the signal energy of said basic detail images, all pixels outside said compact domain having zero value, then said partitioned set of predetermined basic detail images would be such that:
  • every said subset covers the entire domain of said original image, i.e. for every pixel within said original domain there is within every said subset at least one basic detail image the spatial extent of which overlaps with said pixel;
  • all said basic detail images belonging to any particular subset are limited to the same spatial frequency band, said frequency band being defined as the compact region in spatial frequency domain which contains nearly all (say 90%) of the spectral energy of the basic frequency period of said basic detail image;
  • every said subset corresponds to a different spatial frequency band, in such a way that the entire spatial frequency band ranging from -pi through pi radians/pixel along both spatial frequency axes is covered by said spatial frequency bands associated with all said subsets considered within the decomposition;
  • each spatial frequency band associated with one of said subsets may partially overlap the neighboring bands, without being fully included by a frequency band associated with another said subset;
  • the present invention further discloses a processing apparatus for performing the contrast enhancing method(s) according to the present invention on an electronic image representation.
  • the processed image can be visualised by hardcopy recording or through display on a monitor.
  • the electronic image representation is generally obtained by an acquisition apparatus or acquisition section. Then, in the processing section said image representation is decomposed into detail images at multiple resolution levels and a residual image at still lower resolution, these detail images are modified and a processed image is computed by means of a reconstruction algorithm. Next the processed image can be applied to an output section or output apparatus.
  • the acquisition section can be any apparatus or part thereof for obtaining an electronic representation of an image.
  • the acquisition unit can be an apparatus wherein an electronic representation of a image is obtained directly such as a medical scanner, a tomography apparatus, an image intensifier, etc. or alternatively an apparatus wherein an electronic representation of an image is obtained through the intermediary of a storage device such as a radiographic film or a photostimulable phosphor screen.
  • the output section can be a hard-copy recording apparatus such as a laser printer or a thermal printer etc. or it can be a visual display apparatus such as a monitor.
  • the image processing method of the present invention has been developed for the purpose of improving contrast of a digital image over the whole range of signal levels without enlarging the dynamic range in a system for reproducing or displaying an image read-out of a photostimulable phosphor screen.
  • FIG. 1 is a block scheme generally illustrating an apparatus according to the present invention
  • FIG. 2 is specific embodiment of an image acquisition apparatus
  • FIG. 3 is a block scheme illustrating the different steps of the contrast enhancing method
  • FIG. 4a illustrates one way of performing the decomposition step in a method according to the present invention
  • FIG. 4b illustrates an embodiment of a reconstruction algorithm
  • FIG. 4c shows the coefficients of an example of a Gaussian filter
  • FIG. 4d shows a modified embodiment of the reconstruction step
  • FIG. 4e shows another modified embodiment of the reconstruction step
  • FIG. 5a illustrates another embodiment of a decomposition step
  • FIG. 5b illustrates the corresponding reconstruction algorithm
  • FIG. 6a shows a one-dimensional plot of the squared modulus of the transfer functions of a series of low pass filters of decreasing bandwith along one of the spatial frequency coordinate axes
  • FIG. 6b shows the squared modulus of bandpass filter transfer functions corresponding to the subtraction of two low pass filter transfer functions at successively lower resolution
  • FIG. 7 shows the power spectra of pyramidal Gabor functions
  • FIG. 8 is a plot of a specific modifying function that can be used in a method of the present invention.
  • FIG. 9 is a plot of an alternative modifying function
  • FIG. 10a is a plot of one line of an example original image
  • FIG. 10b is a plot of the corresponding line of a contrast enhanced image.
  • An image acquisition unit 1 acquires a digital image by sampling the output signal of an image sensor, such as a CCD sensor, a video camera, or an image scanner, an image intensifying tube, quantizes it using an A/D convertor into an array of pixel values, called raw or original image 2, with pixel values typically 8 to 12 bits long, temporarily stores the pixel values in memory if desired, and transmits the digital image 2 to an image enhancement unit 3, where the image contrast is adaptively enhanced in accordance with the present invention, next the enhanced image 4 is transmitted to the display mapping section 5 which modifies the pixel values according to a contrast curve, such that the relevant image information is presented in an optimal way, when the processed image 6 is visualised on an image output device 7, which produces either a hardcopy on transparent film or on paper, or a viewable image on a display screen (CRT).
  • an image sensor such as a CCD sensor, a video camera, or an image scanner
  • an image intensifying tube quantizes it using an A/D convertor into an array of pixel values, called
  • FIG. 2 A preferred embodiment of image acquisition unit 1 is shown in FIG. 2.
  • a radiation image of an object 11 or part thereof, e.g. a patient is recorded onto a photostimulable phosphor plate by exposing said plate to X-rays originating from an X-ray source 10, transmitted through the object.
  • the photostimulable phosphor plate 13 is conveyed in a cassette 12.
  • the latent image stored in the photostimulable phosphor plate is read out by scanning the phosphor sheet with stimulating rays emitted by a laser 14.
  • the stimulating rays are deflected according to the main scanning direction by means of a galvanometric deflection device 15.
  • the secondary scanning motion is performed by transporting the phosphor sheet in the direction perpendicular to the scanning direction.
  • a light collector 16 directs the light obtained by stimulated emission onto a photomultiplier 17 where it is converted into an electrical signal, which is next sampled by a sample and hold circuit 18, and converted into a 12 bit digital signal by means of an analog to digital converter 19. From there the digital image 2, called raw or original image, is sent to the enhancement section 3.
  • the image enhancement system 3 consists of three main parts, schematically drawn in FIG. 3.
  • a decomposition section 30 the original image 2 is decomposed into a sequence of detail images, which represent the amount of detail present in the original image at multiple resolution levels, from fine to coarse.
  • a residual image 31' may be left.
  • the resulting detail images 31, which represent the amount of local detail at successive resolution levels are next modified in modification section 32 by means of a non-linear mapping operation.
  • the modified detail images 33 are next accumulated at all resolution levels, along with the residual image 31' to compute the enhanced image 4.
  • FIG. 4a A preferred embodiment of the decomposition process is depicted in FIG. 4a.
  • the original image is filtered by means of a low pass filter 41, and subsampled by a factor of two, which is implemented by computing the resulting low resolution approximation image g 1 only at every other pixel position of every alternate row.
  • a detail image b 0 at the finest level is obtained by interpolating the low resolution approximation g 1 with doubling of the number of rows and columns, and pixelwise subtracting the interpolated image from the original image 2.
  • the interpolation is effectuated by the interpolator 42, which inserts a column of zero values every other column, and a row of zero values every other row respectively, and next convolves the extended image with a low pass filter.
  • the subtraction is done by the adder 43.
  • the finest detail image b 0 has the same size as the original image.
  • the next coarser detail image b 1 has only half as many rows and columns as the first detail image b 0 .
  • the maximal spatial frequency of the resulting detail image is only half that of the previous finer detail image, and also the number of columns and rows is halved, in accordance with the Nyquist criterion.
  • a residual image g L 31' is left which can be considered to be a very low resolution approximation of the original image.
  • the filter coefficients of the low pass filter of the preferred embodiment are presented in FIG. 4c. They correspond approximately to the samples of a two dimensional gaussian distribution on a 5 ⁇ 5 grid. The same filter coefficients are used for the low pass filters 41, 41', . . . 41"' at all scales. The same filter kernel with all coefficients multiplied by 4 is also used within the interpolators 42, 42' , . . . 42"'. The factor of 4 compensates for the insertion of zero pixel columns and rows as explained above.
  • the corresponding reconstruction process is depicted in FIG. 4b.
  • the residual image is first interpolated by interpolator 51 to twice its original size and the interpolated image is next pixelwise added to the detail image of the coarsest level b' L-1 , using adder 52.
  • the resulting image is interpolated and added to the next finer detail image. If this process is iterated L times using the unmodified detail images b L-1 . . . b 0 then an image equal to the original image 2 will result. If at the other hand the detail images are modified before reconstruction according to the findings of the present invention, then a contrast enhanced image 4 will result.
  • the interpolators 51, 51' . . . 51"' are identical to those used in the decomposition section.
  • the image quality of the reproduction of a radiologic image read- out of a photostimulable phosphor screen can further be improved by boosting or suppressing the contribution of the detail information as a function of the average approximation values at a certain resolution level.
  • FIG. 4d A first implementation of this procedure is illustrated in FIG. 4d.
  • the modified detail images b' i are pixelwise multiplied by a coefficient which is obtained by applying a lookup table 53" . . . 53"' to the corresponding pixels of the interpolated partially reconstructed image from the previous coarser resolution level.
  • the mapping implemented by the lookup table 53" . . . 53"' is such that the resulting coefficient values are smaller than one in case of relatively small abscissae (corresponding to bright pixels in the partially reconstructed image), and larger than one for relatively large abscissae (corresponding to darker pixels).
  • multipliers 54" . . .
  • the invention further provides a second implementation of this brightness dependent contrast enhancement method that is preferred because of the reduced computational effort; this implementation is illustrated in FIG. 4e.
  • the nonlinear conversion of the partially reconstructed image followed by the inverse conversion after reconstruction essentially modifies the relative importance of fine detail w.r.t. accumulated pixel value at the specified intermediate resolution level, as a function of said accumulated pixel value, which is representative of the brightness at the corresponding position in the final reconstructed image (since said intermediate image is a low resolution approximation of the final image).
  • the inverse conversion guarantees that the overall gradation remains unchanged, i.e. the combined effect of forward and inverse conversion is nihil if the finer detail images added after forward conversion are all zero. As a result fine detail contrast (and also noise) in bright images areas are reduced w.r.t. detail contrast of similar amplitude in dark image regions.
  • the above forward and inverse conversions are commonly implemented by means of a lookup table (55 and 56 resp.).
  • the inverse lookup table may be merged with the lookup table that implements the mapping of signal values into density values to be obtained in the reproduction of a soft- or hardcopy, in order to reduce computation time.
  • FIG. 5a and 5b depict a second embodiment of the decomposition process and the corresponding reconstruction process respectively.
  • the original image is filtered by means of a low pass filter 44, yielding a low resolution approximation of the original image g 1 .
  • a detail image b 0 at the finest level is obtained by pixelwise subtracting the low resolution approximation g 1 from the original image.
  • the bandwidth is decreased by a factor of 2 at every iteration, but other factors can also be considered.
  • a set of low pass filters L i with systematic bandwidth reduction of one octave is easily derived from the filter L 0 at the finest resolution level by successively doubling the number of rows and columns of the filter coefficient kernel, inserting a zero row every other row, and a zero column every other column, respectively. This implementation is computationally efficient, since all multiplications with zero coefficients and subsequent additions can be omitted.
  • the reconstruction according to this second preferred embodiment is depicted in FIG. 5b.
  • this process is executed starting from the unmodified detail images b L-1 . . . b 0 then the original image 2 will result.
  • the detail images are modified before reconstruction according to the findings of the present invention, then a contrast enhanced image will result.
  • the above embodiment is still characterised as multi resolution since the bandwidth is reduced at every subsequent decomposition stage, but it is not pyramidal, since the number of pixels is not reduced accordingly. However this issue does not affect the contrast enhancement performance.
  • Each of the detail images b i as obtained by one of the decomposition methods described above represents the detail information contained in the original image at a specific scale, corresponding to a specific band in spatial frequency.
  • FIG. 6a shows a one-dimensional plot of the squared modulus of the transfer function of the lowpass filters L i along one of the spatial frequency coordinate axes.
  • the cut-off frequency is halved for every subsequent filter.
  • Other reduction factors, such as sqrt(2) may work as well, but the implementation is more complicated, especially if the number of pixels is reduced in accordance with the resolution reduction every subsequent stage.
  • the squared modulus of the bandpass filter transfer functions corresponding to the subtraction of two lowpass filters at successively lower resolution is shown in FIG. 6b. Although the transfer functions substantially overlap, each of them clearly corresponds to a spatial frequency band.
  • a third embodiment of the decomposition and reconstruction process is as follows.
  • the decomposition consists of finding a matrix of weighting coefficients such that the original image is approximated in the least squared error sense as the pixelwise sum of basis images, each basis image multiplied by the appropriate weighting coefficient.
  • the basis images are defined as the product of two one-dimensional basis functions along each of the coordinate axes: cfr. formula (1)
  • Each individual product cfr. formula (2) can be considered as a basis image, with pixel coordinates (k,l).
  • the least squared error solution matrix of weighting coefficients, corresponding to a predetermined set of basis functions is computed using the known technique of singular value decomposition. According to this technique the weighting coefficient matrix W can be expressed as a concatenated matrix product: cfr. formula (3).
  • the set of basis functions h i must be choosen to represent local detail at all scales and at any position within the original image, such that every localised image detail contributes to only a few weighting coefficients w(i,j).
  • the basis functions must have non-zero values only within a limited contiguous abscissa range, the size of this range depending upon the scale for which said basis function is representative.
  • periodic basis functions as used in the Fourier transform are not suited within the context of the present invention.
  • the basis functions must have smooth behaviour, to represent natural details, which excludes basis functions such as used in the Hadamard transform or the Haar transform.
  • a family of basis functions that very effectively represent detail in the context of the present invention are the so-called wavelets.
  • a description of this category of functions is given in:
  • the reconstruction is accomplished by successive matrix multiplication: cfr. formula 4.
  • a still further embodiment of decomposition and reconstruction using orthogonal pyramidal basis functions according to the findings of the present invention is based on the use of quadrature mirror filters.
  • This multi resolution decomposition technique is described in: Adelson E. H., Simoncelli E., and Hingorani R., "Orthogonal pyramid transforms for image coding", Proceedings of SPIE, vol. 845, pp. 50-58, 1987, International Society for Optical Engineering, Bellingham.
  • a family of non-orthogonal basis functions which perform well in representing local detail at multiple resolution scales are the pyramidal Gabor functions: cfr. formula (6).
  • the value N in the above formulas is chosen equal to the column or row size of the original image, which are preferably one less than a power of two: cfr. formula (7).
  • h i (k)*h j (l) All pairwise products of basis functions along horizontal and vertical axes resp. h i (k)*h j (l) are considered to be basic detail images in the context of the present invention, except h 0 (k)*h 0 (l), which is considered to be a basic residual image, having non-zero mean value.
  • the gaussian envelope of these functions guarantees a limited spatial extent, which is required in the context of the present invention, and the size of this spatial extent depends on the scale, so that the whole range of resolution levels are covered.
  • FIG. 7 shows the power spectra of these basis functions, which are all displaced gaussian distributions, each covering approximately a different octave of spatial frequency.
  • a preferred embodiment of the modification section 32 in accordance with the findings of the present invention comprises a memory 61 for temporarily storing the detail images 31 and the residual image 31', and a lookup table 62 wich converts every pixel value x of each detail image into an output value y according to the function:
  • p is chosen within the interval 0 ⁇ p ⁇ 1, preferably within the interval 0.5 ⁇ p ⁇ 0.9.
  • a plot of the above function is presented in FIG. 9. Decreasing the power p 2 will further enhance the contrast of subtle details, but at the same time the noise component will also be amplified.
  • the noise amplification can be limited by choosing a power value p 1 larger than p 2 , preferably 1.0, so that the slope of the mapping function is not extremely steep for the range of very small abscissae in the interval -c . . . c.
  • the cross-over abscissa c should be proportional to the standard deviation of the noise component (assuming additive noise), with a proportionality factor preferably between one and two.
  • mapping function proved to perform very well, but it is clear that an infinite variety of monotonically increasing odd mapping functions can be found that will enhance subtle details without boosting the noise to an excessive level.
  • the main requirement is that the slope of said mapping function is steeper in the subrange of argument values that correspond to small detail image pixel values or coefficient values than it is either in the subrange of very small detail pixel or coefficient values which mostly correspond to noise, or in the range of the larger detail values.
  • F(x) is one of the above described mappings
  • L is the number of resolution levels
  • the detail images are modified starting from the lowest resolution detail image up to the finest level, which is the order in which they are needed in the course of the reconstruction process.
  • the dynamic range of the resulting signal will normally exceed the original range. Therefore the resulting image signal is ultimately reduced to the dynamic range of the original image signal, or even smaller.
  • the above reduction of dynamic range is accomplished by means of a lookup table, which maps said reconstructed image signal to an output signal which represents the desired screen brightness or film density. The mapping is monotonic and may be linear or curved, depending on the desired gradation.
  • FIG. 10a depicts a single line of an original image 2, and FIG. 10b. the corresponding line of a resulting image 4 enhanced according to the first embodiment of decomposition and reconstruction, and the first embodiment of detail modification.
  • FIG. 10b depicts the corresponding line of a resulting image 4 enhanced according to the first embodiment of decomposition and reconstruction, and the first embodiment of detail modification.
  • W VDU T F UDV T ##EQU2## is the resulting weighting coefficient matrix ##EQU3## is the matrix representation of the original image consisting of N ⁇ N pixels, ##EQU4## and where U, V and D are obtained by singular value decomposition of the matrix ##EQU5## in which every column vector represents the samples of one of the basis functions, such that ##EQU6## where the columns of U are the normalised eigenvectors of HH T , where the rows of V are the eigenvectors of H T H, and ⁇ i are the singular values of H in descending order.
  • the diagonal matrix D consists of the inverse singular values 1/ ⁇ i .
  • M s is the number of Gabor functions at every resolution level s
  • N 2 p -1

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